Australia will send a P-8 plane to Tonga on Monday to help assess damage in the country.
The tsunami, caused by an underwater volcano eruption on Saturday, has caused severe damage to communications in Tonga, making it difficult to determine how critical infrastructure has fared.
Mr Morrison said the communication disruption and ash clouds made the situation challenging.
"We're working to get as much support to Tonga as we possibly can," he told 2GB on Monday.
"They're part of our Pacific family, and ... like all of those island nations, we're always there to support and we certainly will be on this occasion.
All Australians and other officials in Tonga have been accounted for.
Defence forces and foreign affairs officials will be working with other countries in the region to provide support.
Mr Morrison has also spoken with his New Zealand counterpart Jacinda Ardern.
The P-8 plane is set to reach Tonga by 9am on Monday, and is part of a coordinated response by Australia and New Zealand.
Pacific Minister Zed Seselja said while there were reports of significant property damage in Tonga, there have been no reports of mass casualties.
"There is still very limited, if any, information coming from the outer islands, and so that will be the focus in coming hours," Senator Seselja told ABC TV.
"We hope that in the next several hours, we'll have a much better assessment of the damage in those outer islands where communications continue to be cut off."
Senator Seselja said other support measures were being prepared and ready to go, including a C-130 plane with humanitarian supplies.
HMAS Adelaide, currently in Sydney, is being deployed to Brisbane where it will be loaded with supplies for Tonga.
"We've been chatting to our US, New Zealand and French partners and others about how we can get a coordinated response going," Senator Seselja said.
"There will be further discussions with the Tongan government to determine how we can support the people of Tonga at this very difficult time, but we stand by to do much more."
A Department of Foreign Affairs spokesman said there were early reports of substantial ash coverage through the Tongan capital of Nuku'alofa along with coastal inundation and damage to infrastructure.
A tsunami warning was issued for parts of Australia's east coast, but was cancelled on Sunday night.
However, the Bureau of Meteorology has warned of unusual sea level changes along the Queensland, Victorian and Tasmanian coasts.
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